Cantor, who appears to have been bipolar, announced in 1885 that he had found a contradiction to his general proposition as to how one should determine whether something is a set. He imparted this contradiction to David Hilbert in 1886. Before he could present it any further, Buali-Forti, in 1887 published it in a paper on other matters. Cantor constructed a flawed proof of another set-theoretic result in 1887 or so. This proof was corrected by Berstein in about 1888. After this Cantor established a very basic result in 1899. This result showed that in his set-theory that there is not set all the his cardinal numbers. Thus there cannot be a set of all sets since a cardinal number is a set.

Both of these anomalies become paradoxes since Cantor eliminated them by added a new axiom, the axiom of “limitation in size,” that is still used in some set-theories but not the one I use. In the informal set-theory I use that can be formalized all such anomalies are eliminated via the notion of classes. That is, if something is not a set, then it is a class. (Class theory is important in constructing models for formal set-theory. It must be O.K. since they give the Fields Medal for results using class theory.)

Remember that on 11/27/2010, I posted an article that attempted to explain via illustration what the mathematical notion of the “infinite” means via “functions” and the notion of the cardinal number for a set A. But, I have simplified my results and no longer need the cardinality notion of <’.

Now when Cantor developed his notions and even today based upon the notion of size of a finite set, one often sees such statements for infinite sets A and B that |A| <’ |B| means that B is “larger” than A. The Church leaders of Cantor’s time thought that his theory of transfinite numbers could be a representation for an infinite God. But, Cantor rejected that notion. (Except for one cased, no one know about nonstandard models until 1966.) In 1899, the rejection was obvious since one could not speak about the set of all such infinities (i.e. cardinal numbers), which would be an obvious possibility for a God model.

Now what I show in this paper is that the measures that I have presented for God’s intelligence and attributes are partial. They are indeed comprehensible measures. But, we can have, as Paul states, only partial measurements of the type I present. One cannot mathematically use nonstandard models as I have done and obtain ultimate measures for God’s intelligence and strength of His attributes. But, looking at the increasing sequence of such measures in their most general form does theologically imply how incomprehensibly “great” in all modeled aspects our God truly is. Something that we all know but now this can be more rationally and formally presented. Hence, my measures of the strength of God’s attributes can only be partially modeled by my approach. My approach and I doubt that any approach can yield a mathematical model that yields an ultimate measure. I’ll notify everyone when the formal paper is available.

Dr. Bob

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